Wong's Equations and Charged Relativistic Particles in Non-Commutative Space

Symmetry Integrability and Geometry-Methods and Applications

article

Herbert Balasin¹  Daniel N. Blaschke²  François Gieres³  Manfred Schweda¹ 

[1] Institute for Theoretical Physics, Vienna University of Technology;Los Alamos National Laboratory, Theory Division;Université de Lyon, Université Claude Bernard Lyon 1 and CNRS/IN2P3, Institut de Physique Nucléaire

关键词: non-commutative geometry;    gauge field theories;    Lagrangian and Hamiltonian formalism;    symmetries and conservation laws;   

DOI  :  10.3842/SIGMA.2014.099

来源: National Academy of Science of Ukraine

【 摘 要 】

In analogy to Wong's equations describing the motion of a charged relativistic point particle in the presence of an external Yang-Mills field, we discuss the motion of such a particle in non-commutative space subject to an external $U_\star(1)$ gauge field. We conclude that the latter equations are only consistent in the case of a constant field strength. This formulation, which is based on an action written in Moyal space, provides a coarser level of description than full QED on non-commutative space. The results are compared with those obtained from the different Hamiltonian approaches. Furthermore, a continuum version for Wong's equations and for the motion of a particle in non-commutative space is derived.

【 授权许可】

Unknown